abstract

Scalar tetraquark states are studied within the diquark–antidiquark picture in a non-relativistic approach. We consider two types of confining potentials, a quadratic and a linear one, to which we also add spin–spin, isospin–isospin, and spin–isospin interactions. We calculate the masses of the scalar diquarks and of the ground state open and hidden charmed and bottom scalar tetraquarks. Our results indicate that the scalar resonances \(D_{0}^{\ast }(2400)\) and \(D_{s}(2632)\) have a sizable tetraquark amount in their wave function, while, on the other hand, it turns out that the scalar states \(D_{s0}^{\ast }(2317)\) and \(X(3915)\) should not be considered as being predominantly diquark–antidiquark bound states. We also investigate the masses of light scalar diquarks and tetraquarks, which are comparable to the measured masses of the light scalar mesons.

abstract

History, status and plans of the search for critical behaviour of strongly interacting matter created in nucleus–nucleus collisions at the CERN Super Proton Synchrotron is reviewed. In particular, it is expected that the search should answer the question whether the critical point of strongly interacting matter exists and, if it does, where it is located. First, the search strategies are presented and a short introduction is given to expected fluctuation signals and to the quantities used by experiments to detect them. The most important background effects are also discussed. Second, relevant experimental results are summarized and discussed. It is intriguing that both the fluctuations of quantities integrated over the full experimental acceptance (event multiplicity and transverse momentum) as well as the bin size dependence of the second factorial moment of pion and proton multiplicities in medium-sized Si+Si collisions at 158\(A\) GeV/\(c\) suggest critical behaviour of the created matter. These results provide strong motivation for the ongoing systematic scan of the phase diagram by the NA61/SHINE experiment at the SPS and the continuing search at the Brookhaven Relativistic Hadron Collider.

abstract

The anomalous magnetic moment of the muon is an important observable that tests radiative corrections of all three observed local gauge forces: electromagnetic, weak and strong interactions. High precision measurements reveal some discrepancy with the most accurate theoretical evaluations of the anomalous magnetic moment. We show in this note that the UV finite theory cannot resolve this discrepancy. We believe that more reliable estimate of the nonperturbative hadronic contribution and the new measurements can resolve the problem.

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Neutrinoless double beta decay is a hypothetical nuclear process actively developed both on theoretical and experimental grounds. In the present paper, we extend the idea discussed in [Phys. Rev. D, 89, 113005 (2014)] where a new channel of this decay has been proposed. In this scenario, neutrinos not only oscillate inside the nucleus but also interact with an external non-uniform magnetic field. We assume that the field rotates about the direction of motion of the neutrino and show that for a certain rotation speed the half-life of the \(0\nu 2\beta \) decay can be significantly shortened. While the presentation in the reference mentioned above was limited to a simplified two-neutrino case, in this work, we investigate the realistic three-neutrino case and perform a detailed numerical study of this process.

abstract

An exact solution of the Einstein field equations given the barotropic equation of state \(p=\omega \rho \) yields two possible models: (1) if \(\omega \lt -1\), we obtain the most general possible anisotropic model for wormholes supported by phantom energy and (2) if \(\omega \gt 0\), we obtain a model for galactic rotation curves. Here, the equation of state represents a perfect fluid which may include dark matter. These results illustrate the power and usefulness of exact solutions.

abstract

We analyze spectral properties of the ultrarelativistic (Cauchy) operator \(|{\mit \Delta }|^{1/2}\), provided its action is constrained exclusively to the interior of the interval \([-1,1] \subset R\). To this end, both analytic and numerical methods are employed. New high-accuracy spectral data are obtained. A direct analytic proof is given that trigonometric functions \(\cos (n\pi x/2)\) and \(\sin (n\pi x)\), for integer \(n\) are not the eigenfunctions of \(|{\mit \Delta }|_D^{1/2}\), \(D=(-1,1)\). This clearly demonstrates that the traditional Fourier multiplier representation of \(|{\mit \Delta }|^{1/2}\) becomes defective, while passing from \(R\) to a bounded spatial domain \(D\subset R\).

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In this article, we investigate the impact of twisted space-time on the photoelectric effect, i.e. , we derive the \(\theta \)-deformed threshold frequency. In such a way, we indicate that the space-time noncommutativity strongly enhances the photoelectric process.

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This research addresses extensive and non-extensive thermodynamics. A comparison between the entropy for both different statistics are presented. The non-extensive parameter, entropic index \(q\), is discussed. We attempt to explore the limit of the non-extensive parameter by comparing the theoretical results with lattice and the available experimental results. The two thermal parameters \(T\), \(\mu _{B}\) are calculated with the freeze-out condition \(S/T^{3}=7\) for different \(q\). The motivation of this research comes from recent non-extensive statistics studies which showed that this standard thermodynamics failed to reproduce the freeze-out parameters. As an application, the black-hole entropy is calculated in the quantum Generalized Uncertainty Principle (GUP) modification form. Black-hole entropy may reveal information about the thermodynamics it belongs. This discrimination is essential to quantify the entropy in the hadron production evolution stage and in the black-hole thermodynamics. It is concluded that lattice QCD reproduces the extensive thermodynamics very well. Also, the black hole appears as an extensive system.

abstract

The stochastic transport in a medium containing traps is described in terms of a subordination technique in which the physical time is regarded as a random quantity given by a density distribution. The traps are assumed to be nonhomogeneously distributed and the subordination method is modified by introducing a position-dependent intensity of a random time distribution. The problem resolves itself to a Langevin equation with a multiplicative noise which defines a process subsequently subordinated to the random time. Moreover, the random stimulation in a form of the Lévy stable distribution is assumed. In the absence of an external potential, the diffusion process is described by the variance which can be finite because an additional multiplicative noise is introduced at some position and effectively makes the system bounded. The diffusion exponent is evaluated and it is demonstrated that it varies with the stability index only if traps are nonhomogeneously distributed. The density distribution converges to a stationary state when a potential is introduced and the relaxation process is analysed for the linear case. The relaxation pattern for the long time always corresponds to the asymptotics of the Mittag–Leffler function but the effective relaxation time strongly depends on the nonhomogeneity parameter.

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Stochastic resonance is a prominent effect consisting in enhancement of a response of a physical system to deterministic driving in the presence of noise. It demonstrates a constructive role the noise may play in increasing the sensitivity of the system to weak signals, and emerges in different theoretical models and experimental situations. We consider this effect in a periodically modulated two-dimensional double-well potential under the influence of an isotropic \(\alpha \)-stable noise, and discuss the performance of various measures used to describe the stochastic resonance in other setups.

abstract

This study is devoted to reveal a simple self-healing, diffusive–dissolution-like mechanism of transient pore’s closing in a model spherical vesicle. It is based on a novel thermodynamic mechanism invented in terms of structural flux–force relations, with Onsager’s coefficients reflecting the main- and cross-effects of nearly one-micrometer-in-diameter pore formation (of linear cross sectional size \(r\)) immersed within the membrane of a spherical vesicle of at least several tens of micrometer in its radius (\(R\)). The closing nanoscopic limit is given by \(r\to 0\). The pore’s formation is envisaged as a kind of bending and excess-area bearing (randomly occurring) failure, contrasting with a homogenizing action of the surface tension, trying to recover an even distribution of the elastic energy accumulated in the membrane. The failure yields at random the subsequent transient pore of a certain characteristic length along which the solution leaks out, with some appreciable speed, until the passage is ultimately closed within a suitable time interval. Inside such a time span, the system relaxes back toward its local equilibrium and uncompressed state until which the pore dissolves, and the before mentioned excess area vanishes. The (slow and non-exponential) relaxation–dissolution behavior bears a diffusion fingerprint, and it can be related with varying osmotic-pressure conditions. Useful connotations with a qualitatively similar biolubrication mechanism in articulating (micelles-containing) systems, down to the nanoscale, have also been pointed out.